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Theorems · Theorem · group theory

AddUnits.neg_val

∀ {α : Type u} [inst : AddMonoid α] (self : AddUnits α), self.neg + ↑self = 0

neg is the left additive inverse of val in the base AddMonoid.

Defined in
Mathlib.Algebra.Group.Units.Defs
Cited by
3 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
AddMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddUnits.neg_add · cited by 17AddUnits.neg_addisAddUnit_iff_exists · cited by 3isAddUnit_iff_existsAddSubmonoid.addUnit_mem_leftNeg · cited by 1AddSubmonoid.addUnit_mem_…AddMonoid · cited by 2864AddMonoidAddUnits · cited by 325AddUnitsAddUnits.val · cited by 248AddUnits.valAddUnits.neg · cited by 14AddUnits.negAddUnits.neg_valCITED BYCITES

Cites4

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Cited by3

Results whose statement or proof uses this declaration.